Magnetic corrections to the boson self-coupling and boson-fermion coupling in the linear sigma model with quarks

TL;DR

This paper investigates how magnetic fields modify boson self-coupling and boson-fermion coupling in the linear sigma model with quarks, revealing modest decreases and addressing gauge invariance and renormalization issues.

Contribution

It provides the first detailed calculation of magnetic field effects on these couplings within the linear sigma model, including arbitrary and strong field regimes, and discusses renormalization and gauge invariance.

Findings

Couplings decrease modestly with increasing magnetic field.

The arbitrary field result depends on the renormalization scale, requiring careful choice.

The boson-fermion coupling modification can be made gauge invariant with Schwinger's phase.

Abstract

We compute the magnetic field-induced modifications to the boson self-coupling and the boson-fermion coupling, in the static limit, using an effective model of QCD, the linear sigma model with quarks. The former is computed for arbitrary field strengths as well as using the strong field approximation. The latter is obtained in the strong field limit. The arbitrary field result for the boson self-coupling depends on the ultraviolet renormalization scale and this dependence cannot be removed by a simple vacuum subtraction. Using the strong field result as a guide, we find the appropriate choice for this scale and discuss the physical implications. The boson-fermion coupling depends on the Schwinger's phase and we show how this phase can be treated consistently in such a way that the magnetic field induced vertex modification is both gauge invariant and can be written with an explicit factor corresponding to energy-momentum conservation for the external particles. Both couplings show a modest decrease with the field strength.